The Intramolecular Field and the Dielectric Constant

Abstract

A statistical calculation of the average internal field in a dielectric is carried out. The following relation is obtained between the dielectric constant, $\ensuremath{\epsilon}$, and the molecular polarizability, ${p}_{0}$: $\frac{\ensuremath{\epsilon}\ensuremath{-}1}{\ensuremath{\epsilon}+2}V=\frac{4\ensuremath{\pi}N{p}_{0}}{3}\frac{1}{1\ensuremath{-}{\ensuremath{\lambda}}_{0\ensuremath{\rho}}}$ where $V$ is the molal volume, $\ensuremath{\rho}$ is the density and ${\ensuremath{\lambda}}_{0}=\frac{32{\ensuremath{\pi}}^{2}{N}^{2}{{P}_{0}}^{2}}{45B}\left(1+\frac{1}{3}\frac{A}{\mathrm{BRT}}\right).$ Here $A$ and $B$ are the constants of a van der Waal type equation of state. This expression becomes identical with the familiar Clausius-Mosotti relation in the limit of zero density. The formula is applied to dielectric constant measurements on several gases.